Tropical Implicitization and Mixed Fiber Polytopes
نویسندگان
چکیده
The software TrIm offers implementations of tropical implicitization and tropical elimination, as developed by Tevelev and the authors. Given a polynomial map with generic coefficients, TrIm computes the tropical variety of the image. When the image is a hypersurface, the output is the Newton polytope of the defining polynomial. TrIm can thus be used to compute mixed fiber polytopes, including secondary polytopes.
منابع مشابه
Tropical Varieties with Polynomial Weights and Corner Loci of Piecewise Polynomials
We find a relation between mixed volumes of several polytopes and the convex hull of their union, deducing it from the following fact: the mixed volume of a collection of polytopes only depends on the product of their support functions (rather than on the individual support functions). For integer polytopes, this dependence is a certain specialization of the isomorphism between two well-known c...
متن کاملCombinatorics and Genus of Tropical Intersections and Ehrhart Theory
Let g1, . . . , gk be tropical polynomials in n variables with Newton polytopes P1, . . . , Pk. We study combinatorial questions on the intersection of the tropical hypersurfaces defined by g1, . . . , gk, such as the f -vector, the number of unbounded faces and (in case of a curve) the genus. Our point of departure is Vigeland’s work [33] who considered the special case k = n− 1 and where all ...
متن کاملOn the Existence of Mixed Fiber Bodies
We give a direct proof of the existence of mixed fiber bodies which is not based upon the reduction to polytopes by continuity. It uses an explicit formula for the support function of a mixed fiber body instead. With the aid of this formula one can also compute the support function of a Newton polytope of a multidimensional resultant and prove a certain monotonicity property for mixed fiber bod...
متن کاملIrrational Mixed Decomposition and Sharp Fewnomial Bounds for Tropical Polynomial Systems
Given convex polytopes P1, . . . , Pr ⊂ R n and finite subsets WI of the Minkowsky sums PI = � i∈I Pi, we consider the quantityN(W) = � I⊂[r] (−1) r−|I|� WI � �. If WI = Z n ∩ PI and P1, . . . , Pn are lattice polytopes in R , then N(W) is the classical mixed volume of P1, . . . , Pn giving the number of complex solutions of a general complex polynomial system with Newton polytopes P1, . . . , ...
متن کاملElimination Theory for Tropical Varieties
Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/0706.0564 شماره
صفحات -
تاریخ انتشار 2007